// Magma code for the lmfdb family of higher genus curves 13.72-45.0.4-4-6.1
// The results are stored in a list of records called 'data'

RecFormat:=recformat<group,gp_id, signature,gen_vectors,conj_classes,genus,dimension,r,g0, passport_label,gen_vect_label, is_hyperelliptic, hyp_involution, is_cyclic_trigonal,cyc_auto,full_auto, full_sign,topological_class,braid_class>;

data:=[];

// Create group as a permutation group, and generate data which is the same for all entries.
gp_id:=[72,45];
H:=SmallGroup(gp_id[1],gp_id[2]); n:=#H; LP:=[]; LG:=[g : g in H]; for i in [1..n] do x:=LG[i]; Tx:=[LG[j]*x : j in [1..n]]; permL:=[]; for j in [1..n] do for k in [1..n] do if Tx[j] eq LG[k] then permL[j]:=k;  break; end if; end for; end for; Append(~LP,permL); end for; G:=PermutationGroup<n|LP>; 
signature:=[0,4,4,6];
genus:=13;
r:=#signature-1;
g0:=signature[1];
dim:=3*g0-3+r;
S:=Sym(gp_id[1]);

// Here we add an action to data.
gen_vectors:=[[37, 45, 41, 42, 38, 43, 44, 40, 39, 46, 54, 50, 51, 47, 52, 53, 49, 48, 55, 63, 59, 60, 56, 61, 62, 58, 57, 64, 72, 68, 69, 65, 70, 71, 67, 66, 10, 18, 14, 15, 11, 16, 17, 13, 12, 1, 9, 5, 6, 2, 7, 8, 4, 3, 28, 36, 32, 33, 29, 34, 35, 31, 30, 19, 27, 23, 24, 20, 25, 26, 22, 21], [72, 64, 68, 67, 71, 66, 65, 69, 70, 63, 55, 59, 58, 62, 57, 56, 60, 61, 54, 46, 50, 49, 53, 48, 47, 51, 52, 45, 37, 41, 40, 44, 39, 38, 42, 43, 27, 19, 23, 22, 26, 21, 20, 24, 25, 36, 28, 32, 31, 35, 30, 29, 33, 34, 9, 1, 5, 4, 8, 3, 2, 6, 7, 18, 10, 14, 13, 17, 12, 11, 15, 16], [23, 24, 22, 26, 27, 25, 20, 21, 19, 32, 33, 31, 35, 36, 34, 29, 30, 28, 5, 6, 4, 8, 9, 7, 2, 3, 1, 14, 15, 13, 17, 18, 16, 11, 12, 10, 59, 60, 58, 62, 63, 61, 56, 57, 55, 68, 69, 67, 71, 72, 70, 65, 66, 64, 41, 42, 40, 44, 45, 43, 38, 39, 37, 50, 51, 49, 53, 54, 52, 47, 48, 46]];
cc:=[7,10,11];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
full_auto:=[144,115];
full_sign:=[0,2,4,12];
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, full_auto:=full_auto, full_sign:=full_sign>);
